Schmid Law Research Articles

Effects of stirring friction on the microstructure, texture and mechanical properties of 7055 aluminum alloy

Aluminum alloys are widely used in aerospace, transportation, and many other fields due to their excellent properties such as lightweight, ultra-strength, and high toughness. This paper analyzed the influence mechanism of friction stir on the microstructure, texture, and mechanical properties to realize the strength and toughness of 7055 aluminum alloys and optimize their deformation process. The results show that the aluminum alloys change from uneven banded grains to uniform and fine equiaxed grains after friction stir processing, and the grain size is refined from 14 μm to 0.71 μm. The high-angle grain boundary and texture intensity present an initial increase but a subsequent decrease due to the combined effect of recrystallization and high-temperature softening caused by the heat input of friction stir processing. The total texture intensity and volume fraction of the friction stir processed aluminum alloys decrease significantly, and the intensity of RtG {110} <110>, A {110} <111>, E {110} <111>, and F {111} <112> texture significantly decrease or disappear, while the Brass (B) {110} <112> texture increases. The yield strength of FSP aluminum alloys decreases with increasing heat input (w/v), which mainly depends on the weakening of the texture strengthening effect. However, the increase of geometrically necessary dislocations (GND) caused by grain boundary sliding leads to the significant improvement of the deformation hardening ability and plasticity of the material. In addition, the effect of texture on the plasticity of aluminum alloys was calculated by using Schmid law. It is found that the equivalent slip factor (ESF) and maximum Schmid factor (μmax) of A, E, and Cu textures are equal to 0. The small ESF and μmax of the S texture are not conducive to the plastic deformation property of materials, while the 1000 × 70 sample with more ESF (8) and μmax (0.41) of the Cube texture ({001} <100>) shows better plasticity.

Twinning behavior and variant selection mechanism of b.c.c tantalum during dynamic plastic deformation

In this paper, the microstructure and twinning behavior of tantalum (Ta) during dynamic plastic deformation (DPD) were jointly analyzed in combination with impact experiments and molecular dynamics simulations, with a focus on the mechanism of variant selection for twinning. The results indicated that twins nucleate at grain boundaries and gradually grows with increasing deformation until it penetrates the entire grain. Due to the difference of grain boundary dislocation density, strain rate and deformation temperature have significant impacts on the quantity and distribution of twins. In addition, at room temperature, nearly half of the twin variants in DPD samples do not conform to Schmid law, and almost all the twin variants in liquid nitrogen samples do not follow to Schmid law. The activation of these non-Schmid variants is mainly affected by the strain coordination. Through this study, we have deepened our understanding of the dynamic microstructural response of Ta under high-speed deformation conditions.

The Action Mechanism of Rolling Texture on the Anisotropic Behavior of a Pure Titanium Plate

This work combined theoretical calculation with experimental characterization to methodically study the anisotropy mechanism and evolution of the plastic behavior of pure titanium. Initially, a constant-strain uniaxial tensile test was used to measure the anisotropy of the yield behavior along the rolling direction (RD) and transverse direction (TD). Subsequently, the information of crystal orientation both before and after deformation was statistically characterized using electron backscatter diffraction (EBSD). Ultimately, the main deformation mechanism was determined by combining Schmid law with an analysis of the variation of SF values of each deformation mode with the angular relationship between the loading axis and the grain’s c-axis. The findings demonstrate that, for each slip system, the variation trend and value of the SF are influenced by the angle formed by the loading axis and the grain’s c- and a-axes. The primary result of dislocation slip activation is the change of the tilt angle of the grain c-axis from ND to TD, but this has little effect on the tilt angle of the grain c-axis from ND to RD. Prismatic &lt;a&gt; slip dominates the tensile deformation along the RD. Pyramidal &lt;a&gt; slip and pyramidal &lt;c+a&gt; slip will be activated during the subsequent hardening, whereas basal &lt;a&gt; slip is difficult to activate. The prismatic &lt;a&gt; slip in the soft-oriented grain will be preferentially activated during the tensile deformation along the TD, and the prismatic &lt;a&gt; slip and pyramidal &lt;a&gt; slip will become the dominant deformation modes during the subsequent hardening. Some soft-oriented grains could activate basal &lt;a&gt; slip and pyramidal &lt;c+a&gt; slip, but dislocation slip is restricted and coordinated by {10-12}ET.

Activation of contraction twins during compression and related texture characteristics in α-titanium

This work demonstrates that axial compression along 0002and101¯0 in individual grains of α-Titanium can effectively activate up to six variants of 112¯2112¯3¯ contraction twins (CT). Compression parallel to 101¯0 primarily introduces 101¯2101¯1¯ type extension twins (ET), orienting the c-axis almost along the compression axis. Further compression activates up to six 112¯2112¯3¯ CT variants, each with a specific orientation having Euler angles of (0°−60°+n60°, 63.5°, 30°), where n is the sequence number of the CT variant. All six CT variants may not be activated during uniaxial compression due to the deviation of the parent grains' c-axis from the compression direction (CD) and deformation heterogeneities. The nucleation and interaction of CT variants lead to the formation of coincident site lattice boundaries with characteristics (θ−uvtw) angle axis pair of 63.5°101¯0−∑7b, 51.2°11¯00−∑23a, 60°112¯1−∑19b, and 77.3°18¯70−∑17b. The activation of multi CT variants and their interaction can contribute to grain fragmentation and texture weakening. From statistical analyses, the nucleation and growth of CT variants appeared to follow the Schmid law. However, deviations from the Schmid behavior occurred by the activation of low Schmid factor CT variants and could be attributed to slip and twin activities in neighbor grains.

Anisotropic mechanism of cold-rolled pure titanium plate during the two-step tensile process of the variable path

The effects of pre-deformation on the macro-mesoscopic deformation characteristics of the titanium plate during variable path tensile were studied by a two-step tensile test and electron backscatter diffraction (EBSD). The Schmid law, Kernel Average Misorientation (KAM), Taylor axis, and In-Grain Misorientation Axis (IGMA) were used to forecast and identify the types and change laws of the activated deformation modes under different loading conditions. The results demonstrated that dislocation slip is the primary cause of the evolution of the basal split texture components. The nucleation and de-twinning of {10–12}ET resulted in the sudden appearance and disappearance of the <0001>//RD texture. The pre-tensile causes a texture redirection that reduces the activability of both prismatic <a> slip and pyramidal <a> slip in the following variable path tensile. Among them, prismatic <a> slip is the dominant deformation mechanism that causes yield and hardening behavior during RD tensile and TD-RD tensile (rolling direction-RD, transeverse direction-TD). A portion of the prismatic <a> slip is preferentially activated in TD tensile and RD-TD tensile deformation, and the deformation is subsequently jointly controlled by the prismatic <a> slip and the pyramidal <a> slip. The pre-tensile along RD promotes nucleation of {10–12} extension twin (ET) during subsequent RD-TD variable path tensile, while tensile along TD-RD coordinates plastic deformation by consuming a significant quantity of {10–12}ET generated during pre-tensile along TD. The formation of slip-assisted twins in neighboring grains is facilitated by the dislocation pile-up at grain boundaries, and the de-twinning phenomenon also cause the local dislocation pile-up to weaken.

A physically-based mixed hardening model for the prediction of the ductility limits of thin metal sheets using a CPFE approach

An advanced Crystal Plasticity Finite Element (CPFE) approach is developed to accurately predict the ductility limit strains of thin metal sheets. This method uses polycrystalline unit cells to represent the metal sheets at the macroscopic level. The macroscopic behavior of these unit cells is determined based on that of the constituent single crystals using the periodic homogenization multiscale scheme. At the single crystal scale, the constitutive framework follows a finite strain rate-independent formulation, with the flow rule governed by the Schmid law. The evolution of the single crystal yield surface is described through a physically-based mixed hardening model, where isotropic hardening is characterized by a dislocation density-based formulation, while kinematic hardening is described by the nonlinear Armstrong–Frederick model. The unit cell ductility limit strains are predicted by the Rice bifurcation criterion. The reliability of the mixed hardening model in accurately reproducing mechanical behavior is confirmed through simulations of uniaxial tension/compression loading. Then, the developed computational strategy is used to investigate the impact of key microstructural hardening parameters on the initiation of localized necking under linear strain paths. The numerical predictions reveal the significant influence of these parameters on the formability of thin metal sheets. Additionally, the analysis of ductility limits under non-linear strain paths demonstrates a strong dependency of the numerical predictions on strain path changes. The numerical predictions obtained by the developed CPFE multiscale strategy are compared with experimental results from the literature. In summary, the proposed approach provides a reliable tool for accurately predicting the ductility limits of thin metal sheets, offering valuable insights for engineering applications.

Investigation of the effect of morphological and crystallographic textures on the ductility limits of thin metal sheets using a CPFEM-based approach

The current contribution investigates the effect of some relevant microstructural parameters (specifically, morphological and crystallographic textures) on the ductility limits of polycrystalline aggregates using the Crystal Plasticity Finite Element Method (CPFEM). The polycrystalline aggregates are assumed to be representative of thin metal sheets and their macroscopic behavior is determined from that of their constituent single crystals on the basis of the periodic homogenization technique. The single crystal behavior is described by a finite strain elastoplastic framework in which the plastic flow rule obeys the classical Schmid law and plastic deformation is solely attributed to the slip on the crystallographic slip systems. The CPFEM is implemented within and in connection with ABAQUS/Standard finite element code. The ductility limits are predicted by the Rice bifurcation theory where strain localization is detected when the macroscopic acoustic tensor becomes singular. Three grain morphologies (namely, cube, random, and elongated morphology) and three initial crystallographic textures (namely, cube, random, and copper orientation) are considered to investigate the effect of morphological and crystallographic textures on the onset of plastic strain localization. The numerical results indicate that the effect of initial crystallographic texture is much more pronounced than that of grain morphology on the predicted ductility limits. In addition, the impact of grain size and sheet thickness are thoroughly analyzed. The research reveals that the trends of the predicted ductility limits are strongly dependent on the size effects.

Influence of grain size on twinning behavior of WE43 magnesium alloy during room-temperature compression deformation

In the present study, room-temperature compression experiments and characterization experiments via optical microstructure (OM), X-ray diffractometer (XRD) and electron backscattered diffraction (EBSD) techniques were conducted on WE43 magnesium (Mg) alloy samples to investigate the grain size effect on twinning behavior. Three couples of solution treatments (823 K for 0.5 h, 798 K for 8 h, 823 K for 16 h, followed by water-quenching at ⁓333 K) were adopted and these solutionized samples are with different grain sizes of 48.5, 72.0 and 120.2 μm, respectively. Results show that {10-12} extension twin (ET) and {11-21} ET serve as major twinning modes during plastic deformation. For all 7.7%-deformed samples, although the volume fractions of {10-12} ETs and {11-21} ETs increase with the increasing grain size. {10-12} ETs are in growth stage, while {11-21} ETs are mainly in nucleation stage and they still maintain narrow and parallel to each other. Besides, {10-12} ETs mainly contribute to the rotation of c-axes of grains towards compression direction, while {11-21} ETs mainly contribute to the formation of a nearly ring-shaped texture component in (0002) pole figure. Twin variants analysis with the assistance of Schmid factor (SF) demonstrates that the activation of twin variants mainly obeys Schmid law. When only {10-12} ETs occur in individual grains, the maximum number of twin variants shows some positive relationship with the increasing grain size. By comparison, when both {10-12} ETs and {11-21} ETs occur in individual grains, the maximum numbers of twin variants are rarely influenced by the increasing grain size.

{332}[formula omitted] twinning in a [formula omitted]-type Ti-Nb alloy over a wide range of strain rates

The {332}〈113〉 twinning in a β-type Ti-25Nb alloy is investigated quantitatively at 10% compression strain over a wide range of strain rate from 10−2 s−1 to 106 s−1, using material testing system, split Hopkinson pressure bar, and gas gun loading. Electron backscatter diffraction data are collected from the postmortem samples to obtain activated twinning systems and twinning strain tensors. With increasing strain rate, yield stress and twin density increase, and twin thickness decreases. At low strain rate, only the twinning systems with high Schmid factor can be activated to form thick twins. However, at medium and high strain rates, certain twinning activation deviates from the Schmid law, and twin thickening is relatively insensitive to Schmid factor. Twinning strain is the highest for the matrix grain orientations near 〈114〉, but approximately zero for the orientations near 〈111〉. Contribution of twinning to plastic strain at medium strain rate is significantly higher than those at low and high strain rates.

Amorphous and anisotropic surface relief formation in tungsten under repeated high-flux hydrogen plasma loads

Facing extreme plasma loads, the structural integrity of the tungsten divertor is crucial for ITER, an engineering marvel in nuclear fusion reactors, to achieve its fusion performance targets. Induced by repeated transient heating from plasmas, the thermal fatigue damage of tungsten–typically accompanied by the formation of surface relief–has been identified as a critical issue but an in-depth understanding is still lacking. Here, we report the formation of amorphous and anisotropic surface relief on ITER-grade tungsten surfaces under ITER-relevant hydrogen plasma loads. Measured by both electron backscatter diffraction over large fields of view and transmission Kikuchi diffraction of site-specific lamellae, such surface relief preferentially forms on grains with {110} planes parallel to the surface. This cannot be explained by the orientation-dependent resolved shear stress according to the Schmid law, threshold displacement energy anisotropy, or oxidation anisotropy. Furthermore, surface relief amorphization is revealed by high-resolution transmission electron microscopy imaging and selected area electron diffraction analysis, and is explained by a novel vacancy-induced amorphization mechanism. The results provide new insights into the thermal fatigue behavior of tungsten for fusion applications.

Quasi-in situ observation of extension twinning of AZ31 magnesium alloy under co-directional dynamic compression

In this paper, twinning nucleation and microstructure evolution of AZ31 magnesium alloy were investigated during the quasi-in situ dynamic compression. The microstructure characterization of the sample before and after deformation was performed via electron backscatter diffraction and transmission electron microscopy. The strain accommodation was estimated by selecting twinning variants and using the geometric compatibility factor (m'). The nucleation behavior of 55.4% extension twinning obeyed Schmid's law under high strain rate compression. The non-Schmidt twinning variants with the highest geometric compatibility factor (m') in the active twinning system of adjacent grains were activated in paired twins that affected the twining nucleation and variant selections.

Statistical investigation of deformation mechanisms in rolled Mg sheet during compression

A statistical investigation of the operating slip/twinning modes and their interactions at grain scale over a large area, containing ~400 grains, was carried out on rolled Mg sheets during room-temperature compression based on EBSD and slip trace analysis. For 10% strain, the slip mode was dominated by basal slip (89%). All the 363 identified twins were tension twins. The concave-up stress−strain curve indicated a twinning-dominated deformation behavior, which was further confirmed by the large twinned area fraction (41%) after the deformation. Most twin variants (79%) followed the Schmid law. The Luster−Morris parameter (m′) did not correlate well to twin transmission. However, most twin transmissions (82%) exhibited larger normalized m (Schmid factor) and m′ values. Additional slip systems were frequently active in the twin domains while not in the parent, which can be explained by Schmid law. Slip transfer across the twin boundaries was also observed. Statistical m analysis revealed that twinning activity was closely related to prismatic slip.

Texture tailoring and microstructure refinement induced by {11−21} and {10−12} twinning in an extruded Mg-Gd alloy

An extruded Mg-17Gd (wt%) alloy with < 0001 > fiber texture was compressed along different directions at room temperature. Electron backscatter diffraction characterization was used to investigate the texture tailoring, twinning and dynamic recrystallization (DRX) behaviors. The results indicate that {10−12} and {11−21} twinning activated. The [0001] pole tilted to compression direction with the strain increasing and twinning dominated the texture transition. Activation of {10−12} twinning can be governed by Schmid law, while it is more appropriate to explain the activation of {11−21} twinning by the basal slip transfer condition in the twinned grains according to the slip trace analysis. In addition, operation of {11−21} twinning can facilitate the nucleation of {10−12} twin in the same grain by changing Schmid factor (SF) in the vicinities of {11−21} twin. Grain refinement occurred in the specimens with large strain and the average grain size decrease from ∼27 µm to ∼12 µm. The mechanism of grain refinement can be summarized as follows: the mobility of twin boundaries will be restricted because of the twin-twin and dislocation-twin interaction and converted to random high angle grain boundaries (HAGBs). The random HAGBs offer the nucleation sites and the strain accumulation within twins offer the driving force which facilitate the formation of DRXed grains at random HAGBs. Additionally, the SF difference within parent grain may result in the formation of HAGBs, and these HAGBs can connected the random HAGBs that result from the dislocation-twin interaction which result in the formation of new grains.

Effect of Sm on twinning behavior of Mg-Gd-Y-Zr alloy at room temperature compression

Twining plays an important role in adjusting the mechanical properties and microstructure in magnesium alloys at room temperature deformation. In this work, the Mg-6Gd-3Y(-3Sm)-0.5Zr alloy was compressed at room temperature to study the effect of the Sm element on the twinning behavior. The results showed that twin of Mg-6Gd-3Y(-3Sm)-0.5Zr alloy after compressive deformation was {10–12} twin. In Mg-6Gd-3Y-0.5Zr alloy, there was coarse parallel twin, while in the Mg-6Gd-3Y-3Sm-0.5Zr alloy, there was a lot of fine cross twin. The variation of activated twin in Mg-6Gd-3Y-3Sm-0.5Zr alloy does not obey Schmid law. The activated cross twin variation in Mg-Gd-Y-Sm-Zr alloy can be divided into single-variant cross twin and multi-variant cross twin, both of which lead to changes in orientation differences. The large number of fine cross twin lead to matrix divided. This strengthened fine grains and the Mg-Gd-Y-Sm-Zr alloy showed high deformation stresses.

Ductility limit prediction for polycrystalline aggregates using a CPFEM-based multiscale framework

The ductility of polycrystalline aggregates is usually limited by two main phenomena: plastic strain localization and void coalescence. The goal of this contribution is to develop a new multiscale framework, based on the crystal plasticity finite element method (CPFEM), for the prediction of ductility limits set by these two phenomena for porous and non-porous polycrystalline aggregates. This numerical framework is based on the combination of crystal plasticity constitutive modeling with the periodic homogenization scheme. Within this strategy, the single crystal constitutive modeling follows a finite strain rate-independent approach, where the plastic flow is governed by the classical Schmid law. Thereby, the competition between the two aforementioned phenomena, which limit ductility, is thoroughly analyzed using the bifurcation theory and a strain-based coalescence criterion. To cover a wide range of mechanical states in this analysis, two types of loadings are applied to the studied aggregates: proportional triaxial stress paths and proportional in-plane strain paths. The developed CPFEM-based framework is well suited to account for essential microstructural features: pre-existence of spherical voids, crystallographic and morphological anisotropy, matrix polycrystallinity and interactions between grains and their surrounding medium. Extensive sensitivity studies are performed to analyze the impact of these microstructural features on the ductility limit predictions. The main trends obtained by classical phenomenological frameworks are extended here within the framework of crystal plasticity constitutive modeling.

Microstructure and twinning behavior of b.c.c tantalum under dynamic plastic deformation

In this paper, dynamic plastic deformation (DPD) of tantalum (Ta) was achieved by split Hopkinson pressure bar and a variety of DPD conditions were set to systematically investigate the microstructure of the deformed samples, focusing on the twinning behavior. Results showed that the deformation conditions have a significant effect on the number and distribution of {112}<111>twins. Compared with {100} and {111} grains, {110} grains are more prone to twinning due to the fewer slip systems. As the strain rate increases or the deformation temperature decreases, the number of twins increases dramatically. In addition, the texture of Ta samples gradually changes from {110} to mixed {100} and {111} textures with the increasing deformation, and the number of twins first increases and then decreases. After calculation, it is found that the selection of twin variants in Ta under DPD not only follows Schmid law but is also influenced by strain coordination. The research in this paper deepens the understanding of tantalum as a material for armour-piercing projectile.

Yield Surfaces and Plastic Potentials for Metals, with Analysis of Plastic Dilatation and Strength Asymmetry in BCC Crystals

Since the 1980s, constitutive modeling has steadily migrated from phenomenological descriptions toward approaches that are based on micromechanics considerations. Despite significant efforts, crystal plasticity remains an open field of research. Among the unresolved issues are the anomalous behavior of metals at low temperatures and the stress upturn at extreme dynamics. This work is focused on the low-temperature responses of body-centered-cubic (bcc) metals, among them, molybdenum (Mo). At these conditions, the plastic flow strength is governed by the motion of screw dislocations. The resultant non-planarity of core structures and slip causes the following: the shear stress includes non-glide components, the Schmid law is violated, there is a tension-compression asymmetry, and the yield surface and plastic potential are clearly decoupled. We find that the behavioral complexities can be explained by atomistically resolved friction coefficients in macroscopic yield and flow. The plastic flow mechanisms establish the departure point into the follow-up analysis of yield surfaces. For example, we know that while the von Mises stress is explained based on energy considerations, we will also show that the stress has a clear geometric interpretation. Moreover, the von Mises stress is just one case within a much broader class of equivalent stresses. Possible correlations among non-Schmid effects (as represented macroscopically by friction coefficients), volume change (i.e., residual elastic dilatation) from dislocation lines, and elastic anisotropy are investigated. Extensions to the shock regime are also established.

Twinning-induced Plasticity Mechanism of α″-martensitic Titanium Alloy

The deformation mechanisms of an α″-martensitic Ti–8Mo alloy were investigated by ex-situ electron microscopy tensile tests. Two deformation twins, {110}〈11¯0〉α″ and {130}〈3¯10〉α″ were simultaneously generated by two pathways: (1) direct from primary laths and (2) via reorientation twins. The generation of deformation twinning is strongly dependent on orientation and follows Schmid's law. The dominant twinning in α″ martensite was determined by comparing the shuffle magnitudes calculated from the lattice parameter and the magnitude of lattice modulation. {110}〈11¯0〉α″ and {130}〈3¯10〉α″ twins are activated simultaneously in Ti alloys with a low β-stabilizer content, such as Ti–8Mo alloy.

In Situ Atomic-Scale Observation of 5-Fold Twin Formation in Nanoscale Crystal under Mechanical Loading.

A 5-fold twin is usually observed in nanostructured metals after mechanical tests and/or annealing treatment. However, the formation mechanism of a 5-fold twin has not been fully elaborated, due to the lack of direct time-resolved atomic-scale observation. Here, by using in situ nanomechanical testing combined with atomistic simulations, we show that sequential twinning slip in varying slip systems and decomposition of high-energy grain boundaries account for the 5-fold twin formation in a nanoscale gold single crystal under bending as well as the reversible formation and dissolution of a 5-fold twin in a nanocrystal with a preexisting twin under tension and shearing. Moreover, we find that the complex stress state in the neck area results in the breakdown of Schmid's law, causing 5-fold twin formation in a gold nanocrystal with a twin boundary parallel to the loading direction. These findings enrich our understanding of the formation process of high-order twin structures in nanostructured metals.

Enhancement of the mechanical properties of textured AZ31 Mg alloy sheets by bimodal-orientation microstructure: Basal orientation and RD-texture

In the present study, a bimodal-orientation microstructure including the basal orientation and RD-texture was prepared by twinning deformation of an AZ31 Mg alloy sheet. Experimental results show that 21%–24% of tension twin boundaries are produced and that the recrystallization content decreased by up to 30.5%–52.0% after hot deformation. The variant selections of island twin and parallel tension twin pairs conform to the Schmid law, while the connected twin pairs and the twin transmitting are controlled by the strain coordination. Twin-free grains are observed because of the accommodation strain controlled by the hard deformation mode. After final post-annealing, the bimodal-orientation microstructure is balanced with a tension twin boundary fraction and recrystallization content of 16.6%–22.2% and 45.0%–74.3%, respectively. Finally, the anisotropy weakening, and improvement of formability are obtained due to the orientation adjustment and work hardening elimination, with the average Lankford values (r‾) decreasing from 2.84 to 0.43 and the IE value increasing from 2.25 to 4.63.